178edo - Revision history

Neutraldown at 02:02, 28 November 2025

2025-11-28T02:02:08Z

← Older revision		Revision as of 02:02, 28 November 2025
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	{{ED intro}}		{{ED intro}}

	178et [[tempering out\|tempers out]] 15625/15552 ([[15625/15552\|kleisma]]) and {{monzo\| -49 28 2 }} in the 5-limit. Using the [[patent val]], it tempers out [[225/224]], [[4375/4374]], and 40960000/40353607 in the 7-limit; [[243/242]], [[3025/3024]], 4375/4356, and 16896/16807 in the 11-limit; [[640/637]], [[1188/1183]], 1625/1617, [[1716/1715]], and [[4096/4095]] in the 13-limit. Using the 178def val, it tempers out [[10976/10935]], 33075/32768, and [[50421/50000]] in the 7-limit; [[441/440]], [[3388/3375]], 4125/4096, and [[8019/8000]] in the 11-limit; [[325/324]], [[625/624]], [[847/845]], [[1287/1280]], and [[1573/1568]] in the 13-limit.		178et [[tempering out\|tempers out]] 15625/15552 ([[15625/15552\|kleisma]]) and {{monzo\| -49 28 2 }} in the 5-limit. Using the [[patent val]], it tempers out [[225/224]], [[4375/4374]], and 40960000/40353607 in the 7-limit; [[243/242]], [[3025/3024]], 4375/4356, and 16896/16807 in the 11-limit; [[640/637]], [[1188/1183]], 1625/1617, [[1716/1715]], and [[4096/4095]] in the 13-limit. Using the 178def val, it tempers out [[10976/10935]], 33075/32768, and [[50421/50000]] in the 7-limit; [[441/440]], [[3388/3375]], [[4125/4096]], and [[8019/8000]] in the 11-limit; [[325/324]], [[625/624]], [[847/845]], [[1287/1280]], and [[1573/1568]] in the 13-limit.

	=== Prime harmonics ===		=== Prime harmonics ===

Lériendil at 16:30, 28 February 2025

2025-02-28T16:30:52Z

← Older revision		Revision as of 16:30, 28 February 2025
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	{{ED intro}}		{{ED intro}}

	178et [[tempering out\|tempers out]] 15625/~~15555~~ ([[15625/15552\|kleisma]]) and {{monzo\| -49 28 2 }} in the 5-limit. Using the [[patent val]], it tempers out [[225/224]], [[4375/4374]], and 40960000/40353607 in the 7-limit; [[243/242]], [[3025/3024]], 4375/4356, and 16896/16807 in the 11-limit; [[640/637]], [[1188/1183]], 1625/1617, [[1716/1715]], and [[4096/4095]] in the 13-limit. Using the 178def val, it tempers out [[10976/10935]], 33075/32768, and [[50421/50000]] in the 7-limit; [[441/440]], [[3388/3375]], 4125/4096, and [[8019/8000]] in the 11-limit; [[325/324]], [[625/624]], [[847/845]], [[1287/1280]], and [[1573/1568]] in the 13-limit.		178et [[tempering out\|tempers out]] 15625/15552 ([[15625/15552\|kleisma]]) and {{monzo\| -49 28 2 }} in the 5-limit. Using the [[patent val]], it tempers out [[225/224]], [[4375/4374]], and 40960000/40353607 in the 7-limit; [[243/242]], [[3025/3024]], 4375/4356, and 16896/16807 in the 11-limit; [[640/637]], [[1188/1183]], 1625/1617, [[1716/1715]], and [[4096/4095]] in the 13-limit. Using the 178def val, it tempers out [[10976/10935]], 33075/32768, and [[50421/50000]] in the 7-limit; [[441/440]], [[3388/3375]], 4125/4096, and [[8019/8000]] in the 11-limit; [[325/324]], [[625/624]], [[847/845]], [[1287/1280]], and [[1573/1568]] in the 13-limit.

	=== Prime harmonics ===		=== Prime harmonics ===

ArrowHead294 at 19:26, 20 February 2025

2025-02-20T19:26:53Z

← Older revision		Revision as of 19:26, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|178~~}}		{{ED intro}}

	178et [[tempering out\|tempers out]] 15625/15555 ([[15625/15552\|kleisma]]) and {{monzo\| -49 28 2 }} in the 5-limit. Using the [[patent val]], it tempers out [[225/224]], [[4375/4374]], and 40960000/40353607 in the 7-limit; [[243/242]], [[3025/3024]], 4375/4356, and 16896/16807 in the 11-limit; [[640/637]], [[1188/1183]], 1625/1617, [[1716/1715]], and [[4096/4095]] in the 13-limit. Using the 178def val, it tempers out [[10976/10935]], 33075/32768, and [[50421/50000]] in the 7-limit; [[441/440]], [[3388/3375]], 4125/4096, and [[8019/8000]] in the 11-limit; [[325/324]], [[625/624]], [[847/845]], [[1287/1280]], and [[1573/1568]] in the 13-limit.		178et [[tempering out\|tempers out]] 15625/15555 ([[15625/15552\|kleisma]]) and {{monzo\| -49 28 2 }} in the 5-limit. Using the [[patent val]], it tempers out [[225/224]], [[4375/4374]], and 40960000/40353607 in the 7-limit; [[243/242]], [[3025/3024]], 4375/4356, and 16896/16807 in the 11-limit; [[640/637]], [[1188/1183]], 1625/1617, [[1716/1715]], and [[4096/4095]] in the 13-limit. Using the 178def val, it tempers out [[10976/10935]], 33075/32768, and [[50421/50000]] in the 7-limit; [[441/440]], [[3388/3375]], 4125/4096, and [[8019/8000]] in the 11-limit; [[325/324]], [[625/624]], [[847/845]], [[1287/1280]], and [[1573/1568]] in the 13-limit.

FloraC: Cleanup and +subsets and supersets

2024-04-25T09:39:58Z

Cleanup and +subsets and supersets

← Older revision		Revision as of 09:39, 25 April 2024
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	{{EDO intro\|178}}		{{EDO intro\|178}}

	~~178edo~~ tempers out 15625/15555 (kleisma) and ~~571919811374025/562949953421312~~ in the 5-limit. Using the patent val, it tempers out 225/224, 4375/4374, and 40960000/40353607 in the 7-limit; 243/242, 3025/3024, 4375/4356, and 16896/16807 in the 11-limit; 640/637, 1188/1183, 1625/1617, 1716/1715, and 4096/4095 in the 13-limit. Using the 178def val, it tempers out 10976/10935, 33075/32768, and 50421/50000 in the 7-limit; 441/440, 3388/3375, 4125/4096, and 8019/8000 in the 11-limit; 325/324, 625/624, 847/845, 1287/1280, and 1573/1568 in the 13-limit.		178et [[tempering out\|tempers out]] 15625/15555 ([[15625/15552\|kleisma]]) and {{monzo\| -49 28 2 }} in the 5-limit. Using the [[patent val]], it tempers out [[225/224]], [[4375/4374]], and 40960000/40353607 in the 7-limit; [[243/242]], [[3025/3024]], 4375/4356, and 16896/16807 in the 11-limit; [[640/637]], [[1188/1183]], 1625/1617, [[1716/1715]], and [[4096/4095]] in the 13-limit. Using the 178def val, it tempers out [[10976/10935]], 33075/32768, and [[50421/50000]] in the 7-limit; [[441/440]], [[3388/3375]], 4125/4096, and [[8019/8000]] in the 11-limit; [[325/324]], [[625/624]], [[847/845]], [[1287/1280]], and [[1573/1568]] in the 13-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|178}}		{{Harmonics in equal\|178}}

			=== Subsets and supersets ===
			Since 178 factors into {{factorization\|178}}, 178edo contains [[2edo]] and [[89edo]] as its subsets.

Eliora at 15:10, 22 October 2023

2023-10-22T15:10:04Z

← Older revision		Revision as of 15:10, 22 October 2023
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	178edo tempers out 15625/15555 (kleisma) and 571919811374025/562949953421312 in the 5-limit. Using the patent val, it tempers out 225/224, 4375/4374, and 40960000/40353607 in the 7-limit; 243/242, 3025/3024, 4375/4356, and 16896/16807 in the 11-limit; 640/637, 1188/1183, 1625/1617, 1716/1715, and 4096/4095 in the 13-limit. Using the 178def val, it tempers out 10976/10935, 33075/32768, and 50421/50000 in the 7-limit; 441/440, 3388/3375, 4125/4096, and 8019/8000 in the 11-limit; 325/324, 625/624, 847/845, 1287/1280, and 1573/1568 in the 13-limit.		178edo tempers out 15625/15555 (kleisma) and 571919811374025/562949953421312 in the 5-limit. Using the patent val, it tempers out 225/224, 4375/4374, and 40960000/40353607 in the 7-limit; 243/242, 3025/3024, 4375/4356, and 16896/16807 in the 11-limit; 640/637, 1188/1183, 1625/1617, 1716/1715, and 4096/4095 in the 13-limit. Using the 178def val, it tempers out 10976/10935, 33075/32768, and 50421/50000 in the 7-limit; 441/440, 3388/3375, 4125/4096, and 8019/8000 in the 11-limit; 325/324, 625/624, 847/845, 1287/1280, and 1573/1568 in the 13-limit.

	=== ~~Odd~~ harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|178}}		{{Harmonics in equal\|178}}

Eliora: Cleanup

2023-10-22T15:09:52Z

Cleanup

← Older revision		Revision as of 15:09, 22 October 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''178edo''' is the [[~~EDO\|~~equal division of the octave]] into~~ 178 parts of 6.7416 cents each. It tempers out 15625/15555 (kleisma) and 571919811374025/562949953421312 in the 5-limit. Using the patent val, it tempers out 225/224, 4375/4374, and 40960000/40353607 in the 7-limit; 243/242, 3025/3024, 4375/4356, and 16896/16807 in the 11-limit; 640/637, 1188/1183, 1625/1617, 1716/1715, and 4096/4095 in the 13-limit. Using the 178def val, it tempers out 10976/10935, 33075/32768, and 50421/50000 in the 7-limit; 441/440, 3388/3375, 4125/4096, and 8019/8000 in the 11-limit; 325/324, 625/624, 847/845, 1287/1280, and 1573/1568 in the 13-limit.		{{EDO intro\|178}}

	== ~~Harmonics~~ ==		178edo tempers out 15625/15555 (kleisma) and 571919811374025/562949953421312 in the 5-limit. Using the patent val, it tempers out 225/224, 4375/4374, and 40960000/40353607 in the 7-limit; 243/242, 3025/3024, 4375/4356, and 16896/16807 in the 11-limit; 640/637, 1188/1183, 1625/1617, 1716/1715, and 4096/4095 in the 13-limit. Using the 178def val, it tempers out 10976/10935, 33075/32768, and 50421/50000 in the 7-limit; 441/440, 3388/3375, 4125/4096, and 8019/8000 in the 11-limit; 325/324, 625/624, 847/845, 1287/1280, and 1573/1568 in the 13-limit.

			=== Odd harmonics ===
	{{Harmonics in equal\|178}}		{{Harmonics in equal\|178}}

	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~

BudjarnLambeth: Added "harmonics in equal" table

2023-06-24T01:44:17Z

Added "harmonics in equal" table

← Older revision		Revision as of 01:44, 24 June 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''178edo''' is the [[EDO\|equal division of the octave]] into 178 parts of 6.7416 cents each. It tempers out 15625/15555 (kleisma) and 571919811374025/562949953421312 in the 5-limit. Using the patent val, it tempers out 225/224, 4375/4374, and 40960000/40353607 in the 7-limit; 243/242, 3025/3024, 4375/4356, and 16896/16807 in the 11-limit; 640/637, 1188/1183, 1625/1617, 1716/1715, and 4096/4095 in the 13-limit. Using the 178def val, it tempers out 10976/10935, 33075/32768, and 50421/50000 in the 7-limit; 441/440, 3388/3375, 4125/4096, and 8019/8000 in the 11-limit; 325/324, 625/624, 847/845, 1287/1280, and 1573/1568 in the 13-limit.		'''178edo''' is the [[EDO\|equal division of the octave]] into 178 parts of 6.7416 cents each. It tempers out 15625/15555 (kleisma) and 571919811374025/562949953421312 in the 5-limit. Using the patent val, it tempers out 225/224, 4375/4374, and 40960000/40353607 in the 7-limit; 243/242, 3025/3024, 4375/4356, and 16896/16807 in the 11-limit; 640/637, 1188/1183, 1625/1617, 1716/1715, and 4096/4095 in the 13-limit. Using the 178def val, it tempers out 10976/10935, 33075/32768, and 50421/50000 in the 7-limit; 441/440, 3388/3375, 4125/4096, and 8019/8000 in the 11-limit; 325/324, 625/624, 847/845, 1287/1280, and 1573/1568 in the 13-limit.

			== Harmonics ==
			{{Harmonics in equal\|178}}

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Plumtree: Infobox ET added

2022-10-04T21:14:34Z

Infobox ET added

← Older revision		Revision as of 21:14, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''178edo''' is the [[EDO\|equal division of the octave]] into 178 parts of 6.7416 cents each. It tempers out 15625/15555 (kleisma) and 571919811374025/562949953421312 in the 5-limit. Using the patent val, it tempers out 225/224, 4375/4374, and 40960000/40353607 in the 7-limit; 243/242, 3025/3024, 4375/4356, and 16896/16807 in the 11-limit; 640/637, 1188/1183, 1625/1617, 1716/1715, and 4096/4095 in the 13-limit. Using the 178def val, it tempers out 10976/10935, 33075/32768, and 50421/50000 in the 7-limit; 441/440, 3388/3375, 4125/4096, and 8019/8000 in the 11-limit; 325/324, 625/624, 847/845, 1287/1280, and 1573/1568 in the 13-limit.		'''178edo''' is the [[EDO\|equal division of the octave]] into 178 parts of 6.7416 cents each. It tempers out 15625/15555 (kleisma) and 571919811374025/562949953421312 in the 5-limit. Using the patent val, it tempers out 225/224, 4375/4374, and 40960000/40353607 in the 7-limit; 243/242, 3025/3024, 4375/4356, and 16896/16807 in the 11-limit; 640/637, 1188/1183, 1625/1617, 1716/1715, and 4096/4095 in the 13-limit. Using the 178def val, it tempers out 10976/10935, 33075/32768, and 50421/50000 in the 7-limit; 441/440, 3388/3375, 4125/4096, and 8019/8000 in the 11-limit; 325/324, 625/624, 847/845, 1287/1280, and 1573/1568 in the 13-limit.

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Fredg999 category edits: Sort key

2022-07-02T21:21:28Z

Sort key

← Older revision		Revision as of 21:21, 2 July 2022
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	'''178edo''' is the [[EDO\|equal division of the octave]] into 178 parts of 6.7416 cents each. It tempers out 15625/15555 (kleisma) and 571919811374025/562949953421312 in the 5-limit. Using the patent val, it tempers out 225/224, 4375/4374, and 40960000/40353607 in the 7-limit; 243/242, 3025/3024, 4375/4356, and 16896/16807 in the 11-limit; 640/637, 1188/1183, 1625/1617, 1716/1715, and 4096/4095 in the 13-limit. Using the 178def val, it tempers out 10976/10935, 33075/32768, and 50421/50000 in the 7-limit; 441/440, 3388/3375, 4125/4096, and 8019/8000 in the 11-limit; 325/324, 625/624, 847/845, 1287/1280, and 1573/1568 in the 13-limit.		'''178edo''' is the [[EDO\|equal division of the octave]] into 178 parts of 6.7416 cents each. It tempers out 15625/15555 (kleisma) and 571919811374025/562949953421312 in the 5-limit. Using the patent val, it tempers out 225/224, 4375/4374, and 40960000/40353607 in the 7-limit; 243/242, 3025/3024, 4375/4356, and 16896/16807 in the 11-limit; 640/637, 1188/1183, 1625/1617, 1716/1715, and 4096/4095 in the 13-limit. Using the 178def val, it tempers out 10976/10935, 33075/32768, and 50421/50000 in the 7-limit; 441/440, 3388/3375, 4125/4096, and 8019/8000 in the 11-limit; 325/324, 625/624, 847/845, 1287/1280, and 1573/1568 in the 13-limit.

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Keenan Pepper category edits: Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

2020-12-04T23:13:13Z

Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

← Older revision		Revision as of 23:13, 4 December 2020
Line 1:		Line 1:
	'''178edo''' is the [[EDO\|equal division of the octave]] into 178 parts of 6.7416 cents each. It tempers out 15625/15555 (kleisma) and 571919811374025/562949953421312 in the 5-limit. Using the patent val, it tempers out 225/224, 4375/4374, and 40960000/40353607 in the 7-limit; 243/242, 3025/3024, 4375/4356, and 16896/16807 in the 11-limit; 640/637, 1188/1183, 1625/1617, 1716/1715, and 4096/4095 in the 13-limit. Using the 178def val, it tempers out 10976/10935, 33075/32768, and 50421/50000 in the 7-limit; 441/440, 3388/3375, 4125/4096, and 8019/8000 in the 11-limit; 325/324, 625/624, 847/845, 1287/1280, and 1573/1568 in the 13-limit.		'''178edo''' is the [[EDO\|equal division of the octave]] into 178 parts of 6.7416 cents each. It tempers out 15625/15555 (kleisma) and 571919811374025/562949953421312 in the 5-limit. Using the patent val, it tempers out 225/224, 4375/4374, and 40960000/40353607 in the 7-limit; 243/242, 3025/3024, 4375/4356, and 16896/16807 in the 11-limit; 640/637, 1188/1183, 1625/1617, 1716/1715, and 4096/4095 in the 13-limit. Using the 178def val, it tempers out 10976/10935, 33075/32768, and 50421/50000 in the 7-limit; 441/440, 3388/3375, 4125/4096, and 8019/8000 in the 11-limit; 325/324, 625/624, 847/845, 1287/1280, and 1573/1568 in the 13-limit.

	[[Category:~~Edo~~]]		[[Category:Equal divisions of the octave]]